Sunday, July 27, 2014

Crafting Systematic-Dialectical, Categorial-Progression Presentations of [Sub-]Totalities -- The Principle of Sequential, Non-Redundant, Supplementary, ‘Determinate Oppositions’, and their Formulation via the Dyadic Seldon Function.



                






Dear Readers,


¡This blog-entry describes, for the first time -- in a general, algorithmic manner -- the F.E.D. method for crafting systematic-dialectical, categorial-progression methods of presentation, starting with the dialectical- algorithmic generation of tables of contents, for dialectical-scientific theorizations of a vast range of the various [sub-]totalities of human experience!


We have already, ‘repletely’ illustrated and instantiated this dialectical method earlier in this blog, e.g. --












We have also illustrated how the tables of content of major dialectical expositions -- e.g., by Hegel, and by Marx -- embody these principles of exposition to a high degree, even though uninformed, at the times of their craftings, by any explicitly algebraic, ideogramic guidance, although, as we have shown, an intuitive, heuristic algorithm for dialectics was applied by both Hegel and Marx -- two very different, but related, dialectical heuristics in their two cases, both of which are captured, generically, in the NQ_ axioms. 


This time, for this blog-entry, the general dialectical algorithm of this dialectical method is the direct object of exposition.

But the exposition of this abstract object will not be richly meaningful except for those who already know, and/or who review, the more concrete instantiations of this method, linked-to above.



I hope you will enjoy these heuristic-algorithmic insights into the crafting of dialectical methods of presentation specific to the ontological content of individual sub-totalities, and, moreover, that you will find use-value in using this dialectical algorithmics heuristic in the crafting of systematic ‘‘‘tables of content’’’ for your own systematic-dialectical expository narratives.



Regards,

Miguel







We will play this out four steps -- steps 0, 1, 2, and 3.  Steps beyond step 3 are analogous to step 3.



First:  *Choose your starting category, or «arché», a, as the simplest, most abstract category capturing the whole of the “organic system” that you want to present, in systematic order -- simplest category to most complex; most abstract category to most ‘thought-concrete’ --   

a20  =  a1  =  a.


Some Notes:   ~a signifies the self-determinate negation/opposite’ of a, i.e., signifies aa = a2.  It does not signify the abstract nothingness, undialectical “negation” of a.  

The expression x ~ y means that category x and category y are dialectical, determinate opposites of one another in terms of key determinations, or characteristics, of the content that they, respectively, connote. 

The expression x ~+~ y means that category x and category y are co-present -- “added together” -- non-amalgamatively, because x and y are qualitatively heterogeneous in terms of the content that they connote.


Then:  *Interact a with itself -- let your mind’s ‘ideo-formation’ of a enact an a [immanent or self-]critique of a’s own shortcomings as a full-detail exposition of the “organic system” that you wish to present -- thereby evoking into your awareness a’s immediate, ‘‘‘next consecutive’’’, supplementary opposite category and counter-example, or ‘‘‘counter-category’’’, b --  

a21  =  a2 a x a  =  a(a)  = ~(a)  =  a ~+~ qaa  =  

a ~+~ b  =  a + b  =  (a & b).

The form '(a & b)' symbolizes more explicitly that we are asserting, as of the end of step 1, that BOTH category a and its 'determinate contra-category', qaa or b, are true for -- are characteristic of -- the "organic system" / sub-totality that we are presenting.   

Category qaa or b is ‘counter-a’ and also ‘‘‘supplement to a’’’ in terms of explicitizing more of the content immanent and implicit in the “organic system” that you wish to present systematically and explicitly.


Next:  *Interact (a ~+~ b) with itself -- let your mind’s ‘ideo-formation’ of (a & b) critique (a & b)’s own shortcomings as a full-detail exposition of the “organic system” that you wish to present -- thereby evoking into your awareness both (1) the category c, representing the categorial combination / unity of a and b, which opposes their initially apparently absolute, radical mutual opposition, and (2) b’s immediate, ‘‘‘next consecutive’’’, supplementary opposite category and counter-example, or ‘‘‘counter-category’’’, d --

a22  =  a4  =

(a2)2  =  (a ~+~ b)2  = (a ~+~ b) x (a ~+~ b)   

=  ~(a ~+~ b)  =
 
b(a ~+~ b)  = 

b x (a ~+~ b)  = 

a ~+~ qba + b ~+~ qbb  =  

a ~+~ b ~+~ c ~+~ d.

Category c synthesizes/reconciles categories b and a:  c  =  qba.

Category d is ‘counter-b’:  d  =  qbb.

In summary, step 2 new category d is ‘contra-b’, and step 2 new category c is ‘combo(b, a)’.

KEY:  But d is also ‘contra’, in some of its key characteristics/determinations, to each and all of a, b, and c before it, not just to b alone -- 

d   ~   c, b, [&] a.


Again:  *Interact (a ~+~ b ~+~ c ~+~ d) with itself -- let your own mind’s ‘ideo-formation’ of (a & b & c & d) enact a[n immanent or self-]critique of
(a ~+~ b ~+~ c ~+~ d)’s own shortcomings as a full-detail comprehension of the “organic system” that you wish to present -- thereby evoking into your awareness:  

(1) category e = qda, representing the categorial combination / unity of a and d, which opposes their initially apparently radical mutual opposition, and;  

(2) category f = qdb, representing the categorial combination / unity of b and d, which opposes their initially apparently radical mutual opposition, and;  

(3) category g = qdc = qdba, representing the categorial combination / unity of d and c, i.e., of d, b and a -- i.e., of all previous opposites, d and b, with the «arché», a -- and which opposes their initially apparently absolute, radical mutual opposition, and;  

(4) the final category of step 3, category h = qdd, which represents d’s immediate, ‘‘‘next consecutive’’’, supplementary opposite category and counter-example, or ‘‘‘counter-category’’’ --

a23  =  a8  =

(a4)2  =  (a ~+~ b ~+~ c ~+~ d)2  =

(a ~+~ b ~+~ c ~+~ d) x (a ~+~ b ~+~ c ~+~ d)  =

~(a ~+~ b ~+~ c ~+~ d)  = 

d(a ~+~ b ~+~ c ~+~ d)  =  

d x (a ~+~ b ~+~ c ~+~ d)  = 

a ~+~ qda + b ~+~ qdb + c ~+~ qdc + d ~+~ qdd  = 

a ~+~ b ~+~ c ~+~ d ~+~ e ~+~ f ~+~ g ~+~ h.

Category e synthesizes/reconciles categories d and a:  e  =  qda.

Category f synthesizes/reconciles categories d and b:  f  =  qdb.

Category g synthesizes/reconciles categories d and c, i.e., categories d and qba:  

g  =  qdc  =  qdba.

Category h is ‘counter-d’:  h  =  qdd.

In summary, category h is ‘contra-d’, category e is ‘combo(d, a)’,

category f is ‘combo(d, b)’, and category g is ‘combo(d, b, a)’.

KEY:  But h is also ‘contra’, in some of its key characteristics/determinations, to each and all of a, b,  c, and d, the «arché» category, and the '"opposites"' categories that have been evoked before it, not just to d alone -- 

h    ~     g, f, e, d, c, b, [&] a.


We have a systematically ordered sequence of 'determinate oppositions' -- built from successive, progressive '''determinate negations''' -- additively combined with their 'determinate reconciliations'.



This 'Dyadic Seldon Function' dialectical method is a method of '''UNPACKING''', step-by-step, the '''dialectical contradictions''' -- the 'determinate oppositions', the 'intra-dualities', or, more generally, the 'intra-MULTI-alities' -- that, together with their [partial and full] dialectical resolutions, are internal to, and implicit within, the connotations of that '''historical [sub-]totality''', of that "organic system", of that domain. 

A dialectical theorization and explanation of that organic system's, of that domain's, of that historical [sub-]totality's present, contemporary existence and mode of self-reproduction is thus being presented, synchronically and systematically.

That organic system's, that domain's, that historical [sub-]totality's inherent  'intra-MULTI-alities' are also immanent to -- implicit in the connotations of -- the beginning, the simplest, the most abstract, the «arché» category of, that '''historical [sub-]totality''' / "organic system" / domain.  







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